Is it permissible for a person who had vowed to give a certain amount of money to another, but didn`t find the latter to donate that money to the mosque?

In principle, the vowing person should abide by his vow as much as possible. Therefore, if he couldn`t find the person that he had made the vow for, then the vow itself is countless and nothing is due on its maker. However, if the latter happens to find the former later on then, he has to give him that money.

What is the ruling on the unification of Adhan?

 All perfect praise be to AllahThe Lord of The Worlds, and may His peace and blessings be upon our Prophet Muhammad and upon all of his family and companions.                                                                                                                                                                                                                                  The unified Adhan is an act of Sunnah performed on behalf of a city's population. In addition, any Masjid that doesn’t have a Mua'than (The person who calls for prayers) and doesn`t raise the Adhan misses the reward of this great act. This is because Adhan should be raised for every group of people. However, the unified Adhan should be called in one Masjid and heard through all other Masjids. And Allah Knows Best.

Is it permissible to make up for missed fast after the beginning of the second half of the month of Sha`ban (the month before Ramadan)?

Yes, it is permissible, but one who had missed fasts should hasten to make up for them. As for the Hadith mentioned in this regard, the prohibition is for offering absolute voluntary fasting. And Allah Knows Best.

Is Lease-to-own through Islamic Bank Permissible?